PSTN gateway outboard call doesn't show name (caller ID)

I set up an outboard caller ID for an extension 123 as Smith. When I call out with a regular VOIP provider, it can show the number and the name Smith, but when I call out with a PSTN gateway, it shows only the number. Where can I change so that the PSTN can show the name?

PSTN gateways are not capable of sending a name or number. The called party will only receive the information (name, and, or number) sent by your provider based on the service you subscribe to. There is no way of changing this.